We say that a semantical function is correlated with a syntactical function F iff for any structure A and any sentence we have A F A .It is proved that for a syntactical function F there is a semantical function correlated with F iff F preserves propositional connectives up to logical equivalence. For a semantical function there is a syntactical function F correlated with iff for any finitely axiomatizable class X the class –1X is also finitely axiomatizable (i.e. iff is (...) continuous in model class topology). (shrink)

Simple formula should contain only few quantifiers. In the paper the methods to estimate quantity and quality of quantifiers needed to express a sentence equivalent to given one.

Priest and others have presented their “most telling” argument for paraconsistent logic: that only paraconsistent logics allow non-trivial inconsistent theories. This is a very prevalent argument; occurring as it does in the work of many relevant and more generally paraconsistent logicians. However this argument can be shown to be unsuccessful. There is a crucial ambiguity in the notion of non-triviality. Disambiguated the most telling reason for paraconsistent logics is either question-begging or mistaken. This highlights an important confusion about the role (...) of logic in our development of our theories of the world. Does logic chart good reasoning or our commitments? We also consider another abductive argument for paraconsistent logics which also is shown to fail. (shrink)

Speakers’ perception of a visual scene influences the language they use to describe it—which objects they choose to mention and how they characterize the relationships between them. We show that visual complexity can either delay or facilitate description generation, depending on how much disambiguating information is required and how useful the scene's complexity can be in providing, for example, helpful landmarks. To do so, we measure speech onset times, eye gaze, and utterance content in a reference production experiment in which (...) the target object is either unique or non-unique in a visual scene of varying size and complexity. Speakers delay speech onset if the target object is non-unique and requires disambiguation, and we argue that this reflects the cost of deciding on a high-level strategy for describing it. The eye-tracking data demonstrate that these delays increase when speakers are able to conduct an extensive early visual search, implying that when speakers scan too little of the scene early on, they may decide to begin speaking before becoming aware that their description is underspecified. Speakers’ content choices reflect the visual makeup of the scene—the number of distractors present and the availability of useful landmarks. Our results highlight the complex role of visual perception in reference production, showing that speakers can make good use of complexity in ways that reflect their visual processing of the scene. (shrink)

A history of logic -- Patterns of reasoning -- A language and its meaning -- A symbolic language -- 1850-1950 mathematical logic -- Modern symbolic logic -- Elements of set theory -- Sets, functions, relations -- Induction -- Turning machines -- Computability and decidability -- Propositional logic -- Syntax and proof systems -- Semantics of PL -- Soundness and completeness -- First order logic -- Syntax and proof systems of FOL -- Semantics of FOL -- More semantics -- Soundness and (...) completeness -- Why is first order logic "First Order"? (shrink)

A fundamental notion in a large part of mathematics is the notion of equicardinality. The language with Hartig quantifier is, roughly speaking, a first-order language in which the notion of equicardinality is expressible. Thus this language, denoted by LI, is in some sense very natural and has in consequence special interest. Properties of LI are studied in many papers. In [BF, Chapter VI] there is a short survey of some known results about LI. We feel that a more extensive exposition (...) of these results is needed. The aim of this paper is to give an overview of the present knowledge about the language LI and list a selection of open problems concerning it. After the Introduction $(\S1)$ , in $\S\S2$ and 3 we give the fundamental results about LI. In $\S4$ the known model-theoretic properties are discussed. The next section is devoted to properties of mathematical theories in LI. In $\S6$ the spectra of sentences of LI are discussed, and $\S7$ is devoted to properties of LI which depend on set-theoretic assumptions. The paper finishes with a list of open problem and an extensive bibliography. The bibliography contains not only papers we refer to but also all papers known to us containing results about the language with Hartig quantifier. Contents. $\S1$ . Introduction. $\S2$ . Preliminaries. $\S3$ . Basic results. $\S4$ . Model-theoretic properties of $LI. \S5$ . Decidability of theories with $I. \S6$ . Spectra of LI- sentences. $\S7$ . Independence results. $\S8$ . What is not yet known about LI. Bibliography. (shrink)

The article reviews the various ramifications in the discussion on leadership, focusing on the view of leadership as relationships between leaders and followers. Three main types of leader-follower relations are discussed, and their specific characteristics are described: regressive relations, symbolic relations, and developmental relations. After analyzing the major implications, as well as the conceptual limitations, of these perspectives, the article suggests directions for a more integrative conceptualization of leader-follower relations.

Two questions are addressed in this article: 1. Why are people attracted to leaders? 2. How are leaders' images construed? The first question is analyzed by using the concept of “deity” as a frame of reference for an “ideal model” of leadership. God as a “screen of projections” can satisfy the believer's fundamental needs and desires, as well as serving as a reference for causal attributions and a provider of transcendental meaning. Using Construal Level Theory, deity, as a frame of (...) reference, also facilitates analysis of the second question. This analysis explains universal principles underlying the leadership construal, and the psychological principles and culture-bound processes relevant to construing different images of leadership in different collectives. (shrink)

Two questions are addressed in this article: 1. Why are people attracted to leaders? 2. How are leaders' images construed? The first question is analyzed by using the concept of “deity” as a frame of reference for an “ideal model” of leadership. God as a “screen of projections” can satisfy the believer's fundamental needs and desires, as well as serving as a reference for causal attributions and a provider of transcendental meaning. Using Construal Level Theory, deity, as a frame of (...) reference, also facilitates analysis of the second question. This analysis explains universal principles underlying the leadership construal, and the psychological principles and culture-bound processes relevant to construing different images of leadership in different collectives. (shrink)

In der Technikethik spielt das Konzept der Verantwortung eine zentrale Rolle. ›Verantwortung‹ ist ein Basiskonzept, das, ähnlich wie die Konzepte ›Pflicht‹ oder ›Schuld‹, in vielfältigen Kontexten gebraucht wird. Dennoch lassen sich einige allgemeine Aussagen über seine Bedeutung treffen. Gerade Autoren, die im Bereich der Technik- und Wissenschaftsethik aktiv sind, haben sich nachdrücklich um eine Klärung des allgemeinen Verantwortungsbegriffs und seiner verschiedenen Aspekte und Gebrauchsweisen bemüht.

The book introduces a conception of discourse ethics, an intersubjectivist version of Kantian ethics. Analyzing contributions from Jürgen Habermas, Karl-Otto Apel, Wolfgang Kuhlmann, Albrecht Wellmer, Robert Alexy, Klaus Günther, Rainer Forst, Marcel Niquet and others, it reconstructs critical discussions on the justification of the principle of morality (part I) and on the various proposals on how to apply it (part II). It defends an alternative model of how discourse ethics can provide guidance under non-ideal circumstances and avoid both arbitrariness and (...) rigorism. (shrink)

Krynicki, M. and M. Mostowski, Decidability problems in languages with Henkin quantifiers, Annals of Pure and Applied Logic 58 149–172.We consider the language L with all Henkin quantifiers Hn defined as follows: Hnx1…xny1…yn φ iff f1…fnx1. ..xn φ, ...,fn). We show that the theory of equality in L is undecidable. The proof of this result goes by interpretation of the word problem for semigroups.Henkin quantifiers are strictly related to the function quantifiers Fn defined as follows: Fnx1…xny1…yn φ iff fx1…xn (...) φ,...,f). In contrast with the first result we show that the theory of equality with all quantifiers Fn is decidable.We also consider decidability problems for other theories in languages L and L. (shrink)

The playful discussion of 'horsemanship' that opens Sir Philip Sidney's Defence of Poesie has been variously interpreted as a straightforward anecdote about the chivalric arts, or an oblique rhetorical flourish, or something in between. This essay suggests a new context for Sidney's exordium by focusing primarily on its affiliation to the genre of the 'Art of Poetry'. In Horace's Ars poetica and other classical, scholastic and Renaissance treatises, horse–men and other unnatural hybrids embody the tension between decorum and poetic liberty. (...) Three major traditions inform this trope: by the Renaissance the centaur could be an allegory of reason's struggle with the passions, an emblem of the poetic imagination, or a figure for compositional hybridity associated, especially, with Lucianic satire. Reading Sidney in the light of these traditions, finally, this essay explores aspects of the centaur's significance in the Defence and the Arcadia, and suggests that this kind of attention to metaphor might provide a bridge between critical and creative modes of Renaissance poetic thought. (shrink)

Methods and equations for analysing the kinetics of enzyme-catalysed reactions were developed at the beginning of the 20th century in two centres in particular; in Paris, by Victor Henri, and, in Berlin, by Leonor Michaelis and Maud Menten. Henri made a detailed analysis of the work in this area that had preceded him, and arrived at a correct equation for the initial rate of reaction. However, his approach was open to the important objection that he took no account of the (...) hydrogen-ion concentration (a subject largely undeveloped in his time). In addition, although he wrote down an expression for the initial rate of reaction and described the hyperbolic form of its dependence on the substrate concentration, he did not appreciate the great advantages that would come from analysis in terms of initial rates rather than time courses. Michaelis and Menten not only placed Henri's analysis on a firm experimental foundation, but also defined the experimental protocol that remains standard today. Here, we review this development, and discuss other scientific contributions of these individuals. The three parts have different authors, as indicated, and do not necessarily agree on all details, in particular about the relative importance of the contributions of Michaelis and Menten on the one hand and of Henri on the other. Rather than force the review into an unrealistic consensus, we consider it appropriate to leave the disagreements visible. (shrink)

Connections between partially ordered connectives and Henkin quantifiers are considered. It is proved that the logic with all partially ordered connectives and the logic with all Henkin quantifiers coincide. This implies that the hierarchy of partially ordered connectives is strongly hierarchical and gives several nondefinability results between some of them. It is also deduced that each Henkin quantifier can be defined by a quantifier of the form equation imagewhat is a strengthening of the Walkoe result. MSC: 03C80.

At Protagoras 353de, Socrates gives three possible reasons for calling some pleasures ‘wrong’. Scholarly attention has focused on the second of these, according to which pleasures are ‘wrong’ when they have negative consequences. This paper argues that the first reason corresponds to beliefs held by Democritus, among others; and that the third reason is the view adopted by Socrates in the dialogue.

We investigate theories of initial segments of the standard models for arithmetics. It is easy to see that if the ordering relation is definable in the standard model then the decidability results can be transferred from the infinite model into the finite models. On the contrary we show that the Σ₂—theory of multiplication is undecidable in finite models. We show that this result is optimal by proving that the Σ₁—theory of multiplication and order is decidable in finite models as well (...) as in the standard model. We show also that the exponentiation function is definable in finite models by a formula of arithmetic with multiplication and that one can define in finite models the arithmetic of addition and multiplication with the concatenation operation. We consider also the spectrum problem. We show that the spectrum of arithmetic with multiplication and arithmetic with exponentiation is strictly contained in the spectrum of arithmetic with addition and multiplication. (shrink)

Floridi’s Theory of Strongly Semantic Information posits the Veridicality Thesis. One motivation is that it can serve as a foundation for information-based epistemology being an alternative to the tripartite theory of knowledge. However, the Veridicality thesis is false, if ‘information’ is to play an explanatory role in human cognition. Another motivation is avoiding the so-called Bar-Hillel/Carnap paradox. But this paradox only seems paradoxical, if ‘information’ and ‘informativeness’ are synonymous, logic is a theory of inference, or validity suffices for rational inference; (...) a, b, and c are false. (shrink)

Open access-introduction into moral philosophy in German language that contains chapters on the concept of morality, on the development and the main positions of normative ethics, on meta-ethics, and on the various fields of applied ethics. One of its distinctive features is that it explicitly reflects on the role of morality and ethics in modern society and that it analyses the import of alternative conceptual and normative positions for determining this role. The book can be freely downloaded from the publisher's (...) website via the URL below. (shrink)